Expression of type Conditional

from the theory of proveit.logic.sets.functions.bijections

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, B, Conditional, f
from proveit.logic import And, Bijections, InSet, Injections, Surjections

# build up the expression from sub-expressions
expr = Conditional(And(InSet(f, Injections(A, B)), InSet(f, Surjections(A, B))), InSet(f, Bijections(A, B)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\left(f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right]\right) \land \left(f \in \left[A \xrightarrow[\text{onto}]{} B\right]\right) \textrm{ if } f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 10 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	14, 8
6	Operation	operator: 10 operands: 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 18
9	ExprTuple	14, 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	Operation	operator: 16 operands: 18
14	Variable
15	Operation	operator: 17 operands: 18
16	Literal
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Variable